Demetrio Labate – författare

Over the last 20 years, multiscale methods and wavelets have revolutionized the field of applied mathematics by providing an efficient means of encoding isotropic phenomena. Directional multiscale systems, particularly shearlets, are now having the same dramatic impact on the encoding of multidimensional signals. Since its introduction about five years ago, the theory of shearlets has rapidly developed and gained wide recognition as the superior way of achieving a truly unified treatment in both a continuous and a digital setting. By now, it has reached maturity as a research field, with rich mathematics, efficient numerical methods, and various important applications.

This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing.  It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics.  This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data.After an introductory chapter surveying the scientific significance of  classical and more advanced multiscale methods, chapters cover such topics asAn overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic groupAn introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spacesMicrolocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional dataMathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities.A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented.Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbookfor graduate courses in applied harmonic analysis.​

This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing.  It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics.  This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data.

After an introductory chapter surveying the scientific significance of  classical and more advanced multiscale methods, chapters cover such topics as

An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic groupAn introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spacesMicrolocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional dataMathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities.

A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented.

Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook

for graduate courses in applied harmonic analysis.​